A036839 RATS(n): Reverse Add Then Sort the digits.

0, 2, 4, 6, 8, 1, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 11, 22, 33, 44, 55, 66, 77, 88, 99, 11, 112, 33, 44, 55, 66, 77, 88, 99, 11, 112, 123, 44, 55, 66, 77, 88, 99, 11, 112, 123, 134, 55, 66, 77, 88, 99, 11, 112, 123, 134, 145, 66, 77

Offset: 0

Author

N. J. A. Sloane, Jan 19 2002

Keywords

• nonn
• base
• nice
• easy
• look

Comments

a(n) = RATS(n), not RATS(a(n-1)).

Row 10 of A288535. - Andrey Zabolotskiy, Jun 14 2017

Examples

			1 -> 1 + 1 = 2, so a(1) = 2; 3 -> 3 + 3 = 6, so a(3) = 6.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..50000 (terms 0..1000 from T. D. Noe)
• R. K. Guy, Conway's RATS and other reversals, Unsolved Problems Column, American Math. Monthly, Vol. 96, pp. 425-428, May 1989.
• Eric Weisstein's World of Mathematics, RATS Sequence

Crossrefs

Cf. A004000, A004185, A288535.

Cf. A161593, A114611, A009994, A004086.

Programs

Haskell

a036839 = a004185 . a056964  -- Reinhard Zumkeller, Mar 14 2012

Maple

read transforms; RATS := n -> digsort(n + digrev(n));

Mathematica

FromDigits[Sort[IntegerDigits[#+FromDigits[Reverse [IntegerDigits[#]]]]]] & /@Range[0,80]  (* Harvey P. Dale, Mar 26 2011 *)

Python

def A036839(n):
    x = str(n+int(str(n)[::-1]))
    return int("".join(sorted(x))) # Indranil Ghosh, Jan 28 2017

Formula

Form m by Reversing the digits of n, Add m to n Then Sort the digits of the sum into increasing order to get a(n).

a(n) = A004185(A056964(n)). [Reinhard Zumkeller, Mar 14 2012]